A174049 Prime numbers of the form x^2+y^2 such that Mobius(x) * Mobius(y) = 1.

2, 13, 29, 37, 53, 101, 173, 197, 293, 421, 541, 677, 709, 1021, 1069, 1117, 1373, 1381, 1429, 1597, 1621, 1669, 1709, 1741, 1789, 1861, 1901, 1933, 2053, 2213, 2269, 2293, 2341, 2381, 2557, 2677, 2749, 2797, 3061, 3109, 3221, 3613, 3637, 3701

Offset

1,1

References

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 844.

Links

Jean-François Alcover, Table of n, a(n) for n = 1..1000

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Marc Deléglise and Joël Rivat, Computing the summation of the Mobius function, Experiment. Math. 5:4 (1996), pp. 291-295.

Primefan, Mobius and Mertens Values For n=1 to 2500

Gérard Villemin, Tables des Nombres de Moebius et de Mertens

Example

2 is in the sequence because 2 = 1^2 + 1^2 and mobius(1)*mobius(1) = 1*1 = 1;
13 is a term because 13 = 2^2 + 3^2 and mobius(2)*mobius(3) = (-1)*(-1) = 1.

Maple

with(numtheory): T:=array(0..50000000): k:=1:for x from 1 to 1000 do: for y from x to 1000 do if mobius(x)* mobius(y)= 1 and isprime(x^2+y^2) then T[k]:=x^2+y^2:k:=k+1 fi od od: mini:=T[1]:ii:=1: for p from 1 to k-1 do for n from 1 to k-1 do if T[n] < mini then mini:= T[n]:ii:=n fi od: print(mini): T[ii]:= 99999999: ii:=1:mini:=T[1] :od:

Mathematica

terms = 1000;
Reap[Do[p = x^2 + y^2; If[PrimeQ[p] && MoebiusMu[x] MoebiusMu[y] == 1, Sow[p]], {x, terms}, {y, x}]][[2, 1]] // Sort // Take[#, terms]& (* Jean-François Alcover, Aug 31 2020 *)

Crossrefs

Cf. A008683.

Sequence in context: A041575 A042917 A366720 * A141336 A253970 A361836

Adjacent sequences: A174046 A174047 A174048 * A174050 A174051 A174052

Keyword

nonn

Author

Michel Lagneau, Mar 06 2010

Extensions

Corrected and edited by Michel Lagneau, Apr 25 2010

Typo in name and missing value inserted by D. S. McNeil, Nov 20 2010

Status

approved